Q: My iPod stops when I touch the click wheel

For an iPod Classic, it's most likely a hardware issue.

Apple may be able to repair it but there would be charge for that.

Start here >  iPod Service Answer Center - Apple Support

If the iPod is not working properly, first do a Reset (restart) on the iPod

Learn how to reset your iPod - Apple Support (see section iPod with a click wheel)

If that does not help (or you already tried that), you may want to do a Restore on the iPod using iTunes.  This erases the iPod, reinstalls its software, and sets it to default settings.

Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support

If the problems still recurs after doing a Restore, the cause may be a hardware problem.  In this case, the click-wheel or the click sensor for the play/pause button (undo the click-wheel) may be faulty.

Also, the iPod (depending on specific model) can receive remote control signals through the headphones jack (from headphones that have remote control buttons on the cord).  While less likely, it's possible the iPod may be getting false signals (to play/pause in this case), from faulty headphones even if headphones do not have remote control buttons on cord.  To rule out faulty headphones, try a different set, to see if the problem goes away.